Analysis of Multinomial Models With Unknown Index Using Data Augmentation

By J. Andrew Royle, R. Dorazio, W. Link. Journal of Computational And Graphical Statistics, 2007

283 citations recorded by the source corpus.

Multinomial models with unknown index (“sample size”) arise in many practical settings. In practice, Bayesian analysis of such models has proved difficult because the dimension of the parameter space is not fixed, being in some cases a function of the unknown index. We describe a data augmentation approach to the analysis of this class of models that provides for a generic and efficient Bayesian implementation. Under this approach, the data are augmented with all-zero detection histories. The resulting augmented dataset is modeled as a zero-inflated version of the complete-data model where an estimable zero-inflation parameter takes the place of the unknown multinomial index. Interestingly, data augmentation can be justified as being equivalent to imposing a discrete uniform prior on the multinomial index. We provide three examples involving estimating the size of an animal population, estimating the number of diabetes cases in a population using the Rasch model, and the motivating example of estimating the number of species in an animal community with latent probabilities of species occurrence and detection.

Subfields: Epidemiology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d37c0db9b2f8786d04665e5066faef1a00419672

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Citations in the corpus

Hierarchical Bayes estimation of species richness and occupancy in spatially replicated surveys (2008, background): “framework developed by Royle et al. (2007). We augment the data”
Spatial capture–recapture models allowing Markovian transience or dispersal (2015, unknown): “…have Markov step EACH time. phi = probability moving phi<-1 # phi = 1, transience # Begin simulation loop for(sim in 1:nsim){ cat("sim: ",sim,fill=TRUE) Xl<-min(X[,1]) - ssbuffer Xu<-max(X[,1])+ ssbuffer Yu<-max(X[,2])+ ssbuffer Yl<-min(X[,2])- ssbuffer # Simulate a population of individuals…”
Density Estimation in a Wolverine Population using Spatial Capture-Recapture Models (2011, methodology): “Although N is arbitrary in that it necessarily increases with the size of S, which we prescribe, the density of points N/area(S) is invariant to S as long as S is sufficiently large, which we can verify by conducting a trial MCMC run.”
Bayesian inference in camera trapping studies for a class of spatial capture-recapture models. (2009, methodology): “Given the augmented data set, the key result (Royle et al. 2007) is that the model for the augmented data is a zero-inflated version of the ‘‘knownN’’ model, i.e., that corresponding to the case where N is known.”
Improving density estimates for elusive carnivores: Accounting for sex-specific detection and movements using spatial capture–recapture models for jaguars in central Brazil (2011, methodology): “…parameters including N and si – the number of individuals and their activity centers – we used a Bayesian analysis by data augmentation of the model (Royle et al., 2007), which was implemented in the program WinBUGS (Gilks et al., 1994), accessed through the program R, version 2.10.1 (R Core…”
Modelling of species distributions, range dynamics and communities under imperfect detection: advances, challenges and opportunities (2017, methodology): “Implementing this model extension can become technically complicated, but a method called “data augmentation” (Royle et al. 2007, Royle and Dorazio 2012) allows simple implementation e.g. in BUGS or JAGS.”